Symmetry adapted ro-vibrational basis functions for variational nuclear motion calculations: TROVE approach

Abstract

We present a general, numerically motivated approach to the construction of symmetry adapted basis functions for solving ro-vibrational Schrödinger equations. The approach is based on the property of the Hamiltonian operator to commute with the complete set of symmetry operators and hence to reflect the symmetry of the system. The symmetry adapted ro-vibrational basis set is constructed numerically by solving a set of reduced vibrational eigenvalue problems. In order to assign the irreducible representations associated with these eigenfunctions, their symmetry properties are probed on a grid of molecular geometries with the corresponding symmetry operations. The transformation matrices are re-constructed by solving over-determined systems of linear equations related to the transformation properties of the corresponding wavefunctions on the grid. Our method is implemented in the variational approach TROVE and has been successfully applied to a number of problems covering the most important molecular symmetry groups. Several examples are used to illustrate the procedure, which can be easily applied to different types of coordinates, basis sets, and molecular systems.

References in corpus (10)

• ExoMol molecular line lists - XVI: The rotation-vibration spectrum of hot H${}_2$S
• ExoMol line lists VII: The rotation-vibration spectrum of phosphine up to 1500 K
• The spectrum of hot methane in astronomical objects using a comprehensive computed line list
• ExoMol line lists VIII: A variationally computed line list for hot formaldehyde
• The ExoMol project: Software for computing large molecular line lists
• A highly accurate {\it ab initio} potential energy surface for methane
• ExoMol molecular line lists - XVII The rotation-vibration spectrum of hot SO${}_3$
• ExoMol line lists XV: A new hot line list for hydrogen peroxide
• Accurate Prediction of the Ammonia Probes of a Variable Proton-to-Electron Mass Ratio
• A hybrid variational-perturbation calculation of the ro-vibrational spectrum of nitric acid

Cited by in corpus (13)

• ExoMol molecular line lists XXXV: a rotation-vibration line list for hot ammonia
• ExoMol line lists -- XXXIX. Ro-vibrational molecular line list for CO${}_2$
• ExoMol molecular line lists -- XXXVII: spectra of acetylene
• ExoMol line lists -- XXXVIII. High-temperature molecular line list of silicon dioxide (SiO${}_2$)
• A Variationally Computed IR Line List for the Methyl Radical CH${}_3$
• ExoMol line lists -- XLI. High-temperature molecular line lists for the alkali metal hydroxides KOH and NaOH
• ExoMol line lists -- XL. Ro-vibrational molecular line list for the hydronium ion (H${}_3$O${}^{+}$)
• Electric quadrupole transitions in carbon dioxide
• ExoMol line lists -- LIX. High-temperature line list for N${}_2$O
• General variational approach to nuclear-quadrupole coupling in rovibrational spectra of polyatomic molecules
• A variationally computed room temperature line list for AsH${}_3$
• Theoretical rotation-vibration spectroscopy of {\it cis}- and {\it trans}-diphosphene (P${}_2$H${}_2$) and the deuterated species P${}_2$HD
• Variational Vibrational States of Methanol (12D)